Integer-valued stochastic volatility

We propose a novel class of count time series models, the mixed Poisson integer-valued stochastic volatility models. The proposed specification, which can be considered as an integer-valued analogue of the discrete-time stochastic volatility model, encompasses a wide range of conditional distributions of counts. We study its probabilistic structure and develop an easily adaptable Markov chain Monte Carlo algorithm, based on the Griddy-Gibbs approach that can accommodate any conditional distribution that belongs to that class. We demonstrate that by considering the cases of Poisson and negative binomial distributions. The methodology is applied to simulated and real data.